What you want, I think, is something that will approximate the color, wetness & acidity of the tomatoes, to act as a good medium for poaching eggs. Like Eleana, I suggest red peppers, but for variationr mixed with pureed sweet potato, squash or pumpkin and a little wine vinegar. Another direction completely is muhamara, apersian sauce of pomegranate syrup and walnuts. Last (or first), look at the comments section of the recipe for tested variations from members who''ve made this dish.

Can you eat tomatillos? I think they would come the closest to the juicy tartness of the tomatoes and would go well with the other seasonings in that dish, either on their own or as a mixture with peppers (roasted or sautéed). You might also need to sweeten the sauce to taste at the end, because tomatillos are usually quite a bit more tart than tomatoes. They are commonly available canned in the Latin American foods section of supermarkets, and at least my local Whole Foods usually has fresh ones also.

Based on the photo, it looks like the title of your recipe is a fancy way to say "Shakshuka", which is eggs poached in a tomato sauce. There are tons of variations to this, and basically all you need is some small amount of flavorful liquid in which to cook the eggs.

Getting away from tomato sauce altogether, you could try a "green" version of this. I loved this one from theKitchn: